Correspondence between Young walls and Young tableaux realizations of crystal bases for the classical Lie algebras

TL;DR

This paper establishes a one-to-one correspondence between Young wall and Young tableau realizations of crystal bases for classical Lie algebras, providing a unified combinatorial framework.

Contribution

It introduces a novel bijection linking two different combinatorial models of crystal bases for classical Lie algebras.

Findings

Established a bijection between Young walls and Young tableaux for crystal bases.

Unified combinatorial models for classical Lie algebra representations.

Facilitated easier visualization and computation of crystal bases.

Abstract

We give a 1-1 correspondence with the Young wall realization and the Young tableau realization of the crystal bases for the classical Lie algebras.